Properties

Label 152.12.0.y.1
Level $152$
Index $12$
Genus $0$
Cusps $4$
$\Q$-cusps $2$

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Invariants

Level: $152$ $\SL_2$-level: $8$
Index: $12$ $\PSL_2$-index:$12$
Genus: $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$
Cusps: $4$ (of which $2$ are rational) Cusp widths $1^{2}\cdot2\cdot8$ Cusp orbits $1^{2}\cdot2$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
$\Q$-gonality: $1$
$\overline{\Q}$-gonality: $1$
Rational cusps: $2$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 8C0

Level structure

$\GL_2(\Z/152\Z)$-generators: $\begin{bmatrix}24&121\\141&108\end{bmatrix}$, $\begin{bmatrix}101&76\\114&47\end{bmatrix}$, $\begin{bmatrix}103&144\\94&5\end{bmatrix}$, $\begin{bmatrix}104&5\\137&88\end{bmatrix}$, $\begin{bmatrix}128&99\\105&66\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 152.24.0-152.y.1.1, 152.24.0-152.y.1.2, 152.24.0-152.y.1.3, 152.24.0-152.y.1.4, 152.24.0-152.y.1.5, 152.24.0-152.y.1.6, 152.24.0-152.y.1.7, 152.24.0-152.y.1.8, 152.24.0-152.y.1.9, 152.24.0-152.y.1.10, 152.24.0-152.y.1.11, 152.24.0-152.y.1.12, 152.24.0-152.y.1.13, 152.24.0-152.y.1.14, 152.24.0-152.y.1.15, 152.24.0-152.y.1.16
Cyclic 152-isogeny field degree: $40$
Cyclic 152-torsion field degree: $2880$
Full 152-torsion field degree: $15759360$

Models

This modular curve is isomorphic to $\mathbb{P}^1$.

Rational points

This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
$X_0(4)$ $4$ $2$ $2$ $0$ $0$

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus
152.24.0.l.1 $152$ $2$ $2$ $0$
152.24.0.n.1 $152$ $2$ $2$ $0$
152.24.0.t.1 $152$ $2$ $2$ $0$
152.24.0.v.1 $152$ $2$ $2$ $0$
152.24.0.bi.1 $152$ $2$ $2$ $0$
152.24.0.bl.1 $152$ $2$ $2$ $0$
152.24.0.bn.1 $152$ $2$ $2$ $0$
152.24.0.bo.1 $152$ $2$ $2$ $0$
152.240.17.bm.1 $152$ $20$ $20$ $17$